Power series methods and statistical limit superior

Abstract

Given a real bounded sequence $x=(x_{j})$ and an infinite matrix $A=(a_{nj})$ Knopp core theorem is equivalent to study the inequality $limsup{Ax} ≤ limsup{x}.$ Recently Fridy and Orhan [6] have considered some variants of this inequality by replacing $limsup{x}$ with statistical limit superior $st - limsup{x}$. In the present paper we examine similar type of inequalities by employing a power series method $P$; a non-matrix sequence-to-function transformation, in place of $A =(a_{nj})$ .